What's the Angle?

Objective: In this activity, you will play a game where you make predictions about angle measurements and make angle measurements on a computer using the software Geometer's SketchPad. The person with the lowest score at the end of the game is the winner.

Directions: Open the file angles on the computer. You will see six different angles on the screen. You are about to play the game What's the Angle? with your partner. Here are the rules:

1. Determine which player begins first.

2. During your turn, state an angle on the screen that you would like your partner to guess its measurement. For example, tell your partner, "I would like you to estimate the measurement of <CRF."

3. Using the table below, both of you separately estimate the measure of the angle, and record your prediction in the table below.

4. Now you will use the computer to measure the angle. To measure an angle, hold the shift key down, and click on the three points that describe the angle, making sure that you click on the vertex point second. The angle measurement will appear on the screen. Click and drag the measurement to a spot directly below the angle. Record the value in the table below.

5. With your partner, state whether the angle you measured is acute, right, or obtuse, and explain how you know.

6. Find the difference between your predicted angle measurement and the actual angle measurement. Record the value in the table below.

7. Repeat this process with the other five angles, and switch turns with your partner to select them. After all six angles have been estimated and measured, you will add up all of the numbers in the difference column and record the total. The player with the least total will be the winner!

 Name of Angle Your Estimate Actual Measurement Type of Angle (Acute, Right, Obtuse) Difference

TOTAL = ____________

Challenges

Directions: Open the file figures on the computer. You will see two different angles at the top of the screen, and two figures at the bottom of the screen. You will drag the points in these diagrams to help you answer some challenging questions.

1. At the top of the screen there is a blue angle <AQW and a red angle <WQB. Drag point A and B around.

a) Without measuring, what type of angles is on the screen? Explain how you know.

b) Suppose we join the two angles by sliding them together at ray QW and form <AQB. Double click on the "Combine Angles" button to see what this angle would look like. Is it possible for <AQB to be an acute angle? How about a right angle? How about an obtuse angle? Explain how you know these answers.

2. The figures at the bottom are a triangle to the left and a quadrilateral to the right.

a) Click and drag the vertex points of the triangle. Is it possible to create a triangle with three acute angles? How about two acute angles? How about one acute angle? How about zero acute angles? Explain how you know.